Rapid calculator for traverse



Oct. 30, 1951 L, J. GOLDSMITH RAPID CALCULATOR FOR TRAVERS E TABLES Filed June 2, 1950 DEP(SIN) LATU:

DEP(SIN) ii .i

INVENTOR.

w 0 G M i M Y B Patented Oct. 30, 1951 UNITED STATES PATENT OFFICE RAPID CALCULATOR FOR TRAVERSE TABLES 1 Claim. 1

This invention relates to a traverse table and to a device for rapidly reading the improved traverse table.

The principal object of the invention is to provide a traverse table containing natural sines and cosines of angles at minute intervals arranged in such a way that the result usually obtained by the involved multipulication of a number by a selected sine or cosine can be quickly and easily obtained by observation or simple addition so that tedious and time-consuming multiplication will be avoided.

Another object is to provide a simple device which can be easily carried in a traverse table book, and which will quickly indicate upon the traverse tables the numbers to be added to produce the desired product of any number multiplied by a selected angle function.

Other objects and advantages reside in the detail construction of the invention, which is designed for simplicity, economy, and efficiency. These will become more apparent from the following description.

In the following detailed description of the invention, reference is had to the accompanying drawing which forms a part hereof. Like numerals refer to like parts in all views of the drawing and throughout the description.

In the drawing:

Fig. 1 is a fragmentary view illustrating a portion of a page selected from the improved traverse tables Fig. 2 illustrates the improved traverse table reading device in place upon one of the tables of Fig. 1;

Fig. 3 is a cross-section, taken on the line 33, Fig. 2; and

Figs. 4 and 5 illustrate positions of the tablereading device in solving a particular problem, to be later described.

The improved traverse table, a page of which is indicated at a, contains tables under heading reading LAT(COS) and DEP(SIN), and over reverse designations of DEP(SIN) and LAT(COS), respectively. The heading LAT(COS) refers to the product obtained by multiplying the length of a line by the natural cosine of the bearing angle of that line. The heading DEP(SIN) refers to the product obtained by multiplying the length of a line by the natural sine of the bearing angle of that line.

The tables list natural sines and cosines of angles multiplied by the numbers from 1 to 9 and arranged in siX vertical columns, as shown at b.

The top horizontal row of numbers in each set of six columns is the sine or cosine of a given angle multiplied by 1, and the bottom horizontal row of the six columns equals the sine or cosine of a given angle multiplied by 9.

Each sine, cosine, or multiple thereof consists of one digit to the left of a decimal point and five digits to the right of the decimal point. The decimal point, which would appear between the two columns of digits at the left, has been omitted.

The improved traverse table can be used by reading directly from the tables; it can be used with a mechanical adding or calculating machine; or it can be used with a special reading device, which will be hereinafter described.

To illustrate the uses of the improved rapid traverse table, let us assume the problem to be solved is to multiply the number 1,234.06 by the cosine of the angle 27 32'. The columns showing the multiples of the cosine of the angle 27 32' are illustrated at the left in Fig. 1.

This problem could be worked by ordinary multiplication by multiplying the cosine 0.88674 by 1,234.06 as follows:

For the usual work the last five figures can be ignored to give 1,094.29 as the sought answer.

The answer for the same problem can be obtained directly from the improved rapid traverse table by simply adding the multiples taken from the table as follows:

Total 1,094.29

guide channels formed in its bottom face. The channels are closed by a backing sheet d which is cemented or otherwise secured over the back of the block 0. The backing sheet at projects slightly above the block and also projectsfor greater distance therebelow to form a depending apron.

A plurality of number strips 6 is provided, there being One number strip slidably mounted in each of the guide channels in the frame block. Each number strip e contains a vertical series of numbers, as indicated at 1, running in sequence and reverse order from the number .9 at the top of the strip downward to the number 1, below which 0 (zero) appears. The vertical spacing of the numbers 1 corresponds to the vertical spacing of the numbers in the columnsb and the upper edge of the backing plate d is positioned to come immediately above a number when the lower edge of the latter is aligned with the .upper edge of the block .0.

-Let us assume we have thesame problem as previouslydiscussed, that is, the multiplication of the cosine of the angle 27 32' (088674) by the number 1.23406. The table-reading device is usedas follows:

The number 1.23406 is set up in reverse order immediately above the block c by shifting the strips 1 so that it reads from left to right 604321, as shown in 2. The reading device is placed on the"LAT(COS) table for 27 32, with the upper edge of the backing strip 01 aligned below the lowermost horizontal line of figures, and with the strips e aligning :with the vertical columns, as shown in Figure 2. A black line g may be imprinted on the tables to facilitate placement of the upper edge of the reading device.

"The numbers appearing on the table immediately above each of the strips e are now added mentally. For instance, the numbers appearing in Fig. 2 are 5, 0, 4, 0, 4, and 4, which added together-total 17. "The 7 is written down as the right digit of the answer and the 1 is carried mentally.

The reading device is now moved one column width directly to the left, as shown in Fig. 4. The numbers now appearing above the strip are added mentally. For instance, the numbers appearing in Fig. 4 are 5, 6,3, and '1, which added give 21, which plus the 1 that was carried give a total of 22. We now write down the 2 as the second from the right digit and carry 2. The

answer-is now built up to 27.

to the left, as shown in-Fig.'*5. The-numbers 3,

6, '7; and 6, appearing above thestrips, are added toygive '22, whi h, plus the 2 carried, equals 24. The 4 is inserted in the answer, thus 427, and the 2 is carried.

The reading device is again moved to the left one column to indicate the numbers 2, 7, and 8, which, plus the 2 carried, equals 19. The 9 is inserted in the answer, thus 9427, and the 1 is carried.

The next moveof the device indicates the numbers 3 and l, which added to the 1 carried equals 10. The zero is inserted tothe answer, thus 09427.

The sixth move of the device indicate the zero at the top of the first column, which added to the 1 carried gives a total of 1, which is inserted as the left-hand numeral of the answer, giving the desired product 1094.27.

The answer obtained differs by 0.02 from the answers obtained by other means, because the numbers in the third decimal place to the right of the decimal point were not taken into consideration. To do this, merely start the rapid calculator one column farther to the right. The numbers then appearing at the end of sliding scales would be:

E Sum.

The purpose of adding these numbers was to determine how much to carry for the first number'that is significant in the answer. Round the 19 down to 20. Throwthe zero away and carry the two. This is the same as adding 0,02 to the previous answer of 1,904.27; hence the answer would be the same as by other methods usin the same accuracy or 1,904.29.

While a specific form of the improvement has been described and illustrated herein, it is to be understood that the same may be varied, within the scopeof the appended claim, without departing from the spirit of the invention.

Having thus described the invention, what is claimed and desired secured by Letters Patent is:

A traverse table comprising: a sheet upon which is imprinted the products ,of the function of an angle multiplied by the numbers from 1 to 9.. arranged one below the. other in increasing sequence to form spaced-apart vertical columns of single digits arranged in horizontal rows, each horizontal row of digits in descending order increasing in value over the next above row by the function of the given angle; a relatively flat block positioned upon said sheet; a. plurality of vertically slidable number strips passing through and projecting above said flat block in'parallel relation, said strips corresponding in number and position to the number and spacing of the ,vertical columns in said table, there being numbers 0 to- 9, inclusive, carried .bytheupper faces of said strip in verticalarrangement adjacent the upper extremities thereof, thenumber on each strip being spaced. tocorrespond to the spacing of the numbers ;.in each columnof said table, and decreasing in value downwardly fromthe upperextremities of the strips; and a relatively thin backing sheet secured over the back of said block and separating the latter from saidsheet and extending below said block to form a lower apron thereon.

LEO JEANGOLDSMITH.

"REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS 

